Numerical computation on Lyapunov characteristic exponents of nonlinear vibration for a nano-oscillator

A model of nonlinear vibration for a nano-oscillator was developed. Lyapunov characteristic exponents (LCEs) provide quantitative criteria allowing one to distinguish between regular and chaotic behaviors for the dynamic system. It is difficult to perform numerical integration in terms of standard explicit Runge-Kutta method to obtain the converged LCEs when the motion of system is chaotic. The implicit and symplectic Runge-Kutta approach was presented to solve the differential equations in which the norm of Lyapunov direction vector is corrected to avoid the emergence of overflow error, and the converged LCEs can be solved by means of this algorithm.